Welcome to the forums, I hope that you will find this website to be of use as you explore the world of professional aviation.
I went through the program some time ago and I was able to put some money down, so my payment was about $375 per month. I found the payment to be large, but doable. When I graduated from the program instructors did not make as much and starting pay at the regionals was not as much, so I would say that our positions are rather similar. I was able to buckle down and make extra payments. I saved money wherever I could, put it towards my loan and was able to pay off my loan seven years early. So yes, it can absolutely be done.
Something to keep in mind is ATP’s Tuition Assistance Program. You can easily find it on the ATP website, but the gist of it is this: After you graduate ATP you get hired there as an instructor as part of their guaranteed CFI job program. Between 300 to 500 hours of total time you will interview with one or several of the airlines in the Tuition Assistance Program. After you pass the interview and commit to a particular airline you will receive an additional $5 per hour of flight time that is paid by the airline and applied directly to your loan. So, if you fly 80 hours one month your future airline will pay $400 of your tuition payment the following month, thus leaving you with only $200 to pay that month. It doesn’t stop there, once you transition to the airline they continue to make $500 monthly payments to your loan for at least the next year. Once you complete your first year at the airline your pay will go up to a level where you will more easily be able to afford the payments.
In regards to your other question, airline pilots, corporate pilots and cargo pilots all have to have the exact same ratings, so a program like ATP’s will get you the credentials necessary to apply for any of those jobs. Do keep in mind though that the Tuition Assistance Program only applies to students that are headed towards an airline that is in that program. You could of course always partake in the program, fulfill your year long commitment to the airline and then look for a corporate gig if that is what your heart is set on.
I hope all of this helps and makes sense, feel free to ask any and all questions that you can think of.